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  <section id="module-sympy.physics.optics.waves">
<span id="waves"></span><h1>Waves<a class="headerlink" href="#module-sympy.physics.optics.waves" title="Permalink to this headline">¶</a></h1>
<p>This module has all the classes and functions related to waves in optics.</p>
<p><strong>Contains</strong></p>
<ul class="simple">
<li><p>TWave</p></li>
</ul>
<dl class="py class">
<dt class="sig sig-object py" id="sympy.physics.optics.waves.TWave">
<em class="property"><span class="pre">class</span> </em><span class="sig-prename descclassname"><span class="pre">sympy.physics.optics.waves.</span></span><span class="sig-name descname"><span class="pre">TWave</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="o"><span class="pre">*</span></span><span class="n"><span class="pre">args</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/sympy/sympy/blob/00d6469eafdd4aac346a0b598184c15f2560dbe5/sympy/physics/optics/waves.py#L20-L325"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#sympy.physics.optics.waves.TWave" title="Permalink to this definition">¶</a></dt>
<dd><p>This is a simple transverse sine wave travelling in a one-dimensional space.
Basic properties are required at the time of creation of the object,
but they can be changed later with respective methods provided.</p>
<dl class="field-list">
<dt class="field-odd">Raises</dt>
<dd class="field-odd"><p><strong>ValueError</strong> : When neither frequency nor time period is provided</p>
<blockquote>
<div><p>or they are not consistent.</p>
</div></blockquote>
<p><strong>TypeError</strong> : When anything other than TWave objects is added.</p>
</dd>
</dl>
<p class="rubric">Explanation</p>
<p>It is represented as <span class="math notranslate nohighlight">\(A \times cos(k*x - \omega \times t + \phi )\)</span>,
where <span class="math notranslate nohighlight">\(A\)</span> is the amplitude, <span class="math notranslate nohighlight">\(\omega\)</span> is the angular frequency,
<span class="math notranslate nohighlight">\(k\)</span> is the wavenumber (spatial frequency), <span class="math notranslate nohighlight">\(x\)</span> is a spatial variable
to represent the position on the dimension on which the wave propagates,
and <span class="math notranslate nohighlight">\(\phi\)</span> is the phase angle of the wave.</p>
<p class="rubric">Arguments</p>
<dl class="simple">
<dt>amplitude<span class="classifier">Sympifyable</span></dt><dd><p>Amplitude of the wave.</p>
</dd>
<dt>frequency<span class="classifier">Sympifyable</span></dt><dd><p>Frequency of the wave.</p>
</dd>
<dt>phase<span class="classifier">Sympifyable</span></dt><dd><p>Phase angle of the wave.</p>
</dd>
<dt>time_period<span class="classifier">Sympifyable</span></dt><dd><p>Time period of the wave.</p>
</dd>
<dt>n<span class="classifier">Sympifyable</span></dt><dd><p>Refractive index of the medium.</p>
</dd>
</dl>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy</span> <span class="kn">import</span> <span class="n">symbols</span>
<span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy.physics.optics</span> <span class="kn">import</span> <span class="n">TWave</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">A1</span><span class="p">,</span> <span class="n">phi1</span><span class="p">,</span> <span class="n">A2</span><span class="p">,</span> <span class="n">phi2</span><span class="p">,</span> <span class="n">f</span> <span class="o">=</span> <span class="n">symbols</span><span class="p">(</span><span class="s1">&#39;A1, phi1, A2, phi2, f&#39;</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">w1</span> <span class="o">=</span> <span class="n">TWave</span><span class="p">(</span><span class="n">A1</span><span class="p">,</span> <span class="n">f</span><span class="p">,</span> <span class="n">phi1</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">w2</span> <span class="o">=</span> <span class="n">TWave</span><span class="p">(</span><span class="n">A2</span><span class="p">,</span> <span class="n">f</span><span class="p">,</span> <span class="n">phi2</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">w3</span> <span class="o">=</span> <span class="n">w1</span> <span class="o">+</span> <span class="n">w2</span>  <span class="c1"># Superposition of two waves</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">w3</span>
<span class="go">TWave(sqrt(A1**2 + 2*A1*A2*cos(phi1 - phi2) + A2**2), f,</span>
<span class="go">    atan2(A1*sin(phi1) + A2*sin(phi2), A1*cos(phi1) + A2*cos(phi2)))</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">w3</span><span class="o">.</span><span class="n">amplitude</span>
<span class="go">sqrt(A1**2 + 2*A1*A2*cos(phi1 - phi2) + A2**2)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">w3</span><span class="o">.</span><span class="n">phase</span>
<span class="go">atan2(A1*sin(phi1) + A2*sin(phi2), A1*cos(phi1) + A2*cos(phi2))</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">w3</span><span class="o">.</span><span class="n">speed</span>
<span class="go">299792458*meter/(second*n)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">w3</span><span class="o">.</span><span class="n">angular_velocity</span>
<span class="go">2*pi*f</span>
</pre></div>
</div>
<dl class="py property">
<dt class="sig sig-object py" id="sympy.physics.optics.waves.TWave.amplitude">
<em class="property"><span class="pre">property</span> </em><span class="sig-name descname"><span class="pre">amplitude</span></span><a class="headerlink" href="#sympy.physics.optics.waves.TWave.amplitude" title="Permalink to this definition">¶</a></dt>
<dd><p>Returns the amplitude of the wave.</p>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy</span> <span class="kn">import</span> <span class="n">symbols</span>
<span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy.physics.optics</span> <span class="kn">import</span> <span class="n">TWave</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">A</span><span class="p">,</span> <span class="n">phi</span><span class="p">,</span> <span class="n">f</span> <span class="o">=</span> <span class="n">symbols</span><span class="p">(</span><span class="s1">&#39;A, phi, f&#39;</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">w</span> <span class="o">=</span> <span class="n">TWave</span><span class="p">(</span><span class="n">A</span><span class="p">,</span> <span class="n">f</span><span class="p">,</span> <span class="n">phi</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">w</span><span class="o">.</span><span class="n">amplitude</span>
<span class="go">A</span>
</pre></div>
</div>
</dd></dl>

<dl class="py property">
<dt class="sig sig-object py" id="sympy.physics.optics.waves.TWave.angular_velocity">
<em class="property"><span class="pre">property</span> </em><span class="sig-name descname"><span class="pre">angular_velocity</span></span><a class="headerlink" href="#sympy.physics.optics.waves.TWave.angular_velocity" title="Permalink to this definition">¶</a></dt>
<dd><p>Returns the angular velocity of the wave,
in radians per second.</p>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy</span> <span class="kn">import</span> <span class="n">symbols</span>
<span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy.physics.optics</span> <span class="kn">import</span> <span class="n">TWave</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">A</span><span class="p">,</span> <span class="n">phi</span><span class="p">,</span> <span class="n">f</span> <span class="o">=</span> <span class="n">symbols</span><span class="p">(</span><span class="s1">&#39;A, phi, f&#39;</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">w</span> <span class="o">=</span> <span class="n">TWave</span><span class="p">(</span><span class="n">A</span><span class="p">,</span> <span class="n">f</span><span class="p">,</span> <span class="n">phi</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">w</span><span class="o">.</span><span class="n">angular_velocity</span>
<span class="go">2*pi*f</span>
</pre></div>
</div>
</dd></dl>

<dl class="py property">
<dt class="sig sig-object py" id="sympy.physics.optics.waves.TWave.frequency">
<em class="property"><span class="pre">property</span> </em><span class="sig-name descname"><span class="pre">frequency</span></span><a class="headerlink" href="#sympy.physics.optics.waves.TWave.frequency" title="Permalink to this definition">¶</a></dt>
<dd><p>Returns the frequency of the wave,
in cycles per second.</p>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy</span> <span class="kn">import</span> <span class="n">symbols</span>
<span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy.physics.optics</span> <span class="kn">import</span> <span class="n">TWave</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">A</span><span class="p">,</span> <span class="n">phi</span><span class="p">,</span> <span class="n">f</span> <span class="o">=</span> <span class="n">symbols</span><span class="p">(</span><span class="s1">&#39;A, phi, f&#39;</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">w</span> <span class="o">=</span> <span class="n">TWave</span><span class="p">(</span><span class="n">A</span><span class="p">,</span> <span class="n">f</span><span class="p">,</span> <span class="n">phi</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">w</span><span class="o">.</span><span class="n">frequency</span>
<span class="go">f</span>
</pre></div>
</div>
</dd></dl>

<dl class="py property">
<dt class="sig sig-object py" id="sympy.physics.optics.waves.TWave.phase">
<em class="property"><span class="pre">property</span> </em><span class="sig-name descname"><span class="pre">phase</span></span><a class="headerlink" href="#sympy.physics.optics.waves.TWave.phase" title="Permalink to this definition">¶</a></dt>
<dd><p>Returns the phase angle of the wave,
in radians.</p>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy</span> <span class="kn">import</span> <span class="n">symbols</span>
<span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy.physics.optics</span> <span class="kn">import</span> <span class="n">TWave</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">A</span><span class="p">,</span> <span class="n">phi</span><span class="p">,</span> <span class="n">f</span> <span class="o">=</span> <span class="n">symbols</span><span class="p">(</span><span class="s1">&#39;A, phi, f&#39;</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">w</span> <span class="o">=</span> <span class="n">TWave</span><span class="p">(</span><span class="n">A</span><span class="p">,</span> <span class="n">f</span><span class="p">,</span> <span class="n">phi</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">w</span><span class="o">.</span><span class="n">phase</span>
<span class="go">phi</span>
</pre></div>
</div>
</dd></dl>

<dl class="py property">
<dt class="sig sig-object py" id="sympy.physics.optics.waves.TWave.speed">
<em class="property"><span class="pre">property</span> </em><span class="sig-name descname"><span class="pre">speed</span></span><a class="headerlink" href="#sympy.physics.optics.waves.TWave.speed" title="Permalink to this definition">¶</a></dt>
<dd><p>Returns the propagation speed of the wave,
in meters per second.
It is dependent on the propagation medium.</p>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy</span> <span class="kn">import</span> <span class="n">symbols</span>
<span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy.physics.optics</span> <span class="kn">import</span> <span class="n">TWave</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">A</span><span class="p">,</span> <span class="n">phi</span><span class="p">,</span> <span class="n">f</span> <span class="o">=</span> <span class="n">symbols</span><span class="p">(</span><span class="s1">&#39;A, phi, f&#39;</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">w</span> <span class="o">=</span> <span class="n">TWave</span><span class="p">(</span><span class="n">A</span><span class="p">,</span> <span class="n">f</span><span class="p">,</span> <span class="n">phi</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">w</span><span class="o">.</span><span class="n">speed</span>
<span class="go">299792458*meter/(second*n)</span>
</pre></div>
</div>
</dd></dl>

<dl class="py property">
<dt class="sig sig-object py" id="sympy.physics.optics.waves.TWave.time_period">
<em class="property"><span class="pre">property</span> </em><span class="sig-name descname"><span class="pre">time_period</span></span><a class="headerlink" href="#sympy.physics.optics.waves.TWave.time_period" title="Permalink to this definition">¶</a></dt>
<dd><p>Returns the temporal period of the wave,
in seconds per cycle.</p>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy</span> <span class="kn">import</span> <span class="n">symbols</span>
<span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy.physics.optics</span> <span class="kn">import</span> <span class="n">TWave</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">A</span><span class="p">,</span> <span class="n">phi</span><span class="p">,</span> <span class="n">f</span> <span class="o">=</span> <span class="n">symbols</span><span class="p">(</span><span class="s1">&#39;A, phi, f&#39;</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">w</span> <span class="o">=</span> <span class="n">TWave</span><span class="p">(</span><span class="n">A</span><span class="p">,</span> <span class="n">f</span><span class="p">,</span> <span class="n">phi</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">w</span><span class="o">.</span><span class="n">time_period</span>
<span class="go">1/f</span>
</pre></div>
</div>
</dd></dl>

<dl class="py property">
<dt class="sig sig-object py" id="sympy.physics.optics.waves.TWave.wavelength">
<em class="property"><span class="pre">property</span> </em><span class="sig-name descname"><span class="pre">wavelength</span></span><a class="headerlink" href="#sympy.physics.optics.waves.TWave.wavelength" title="Permalink to this definition">¶</a></dt>
<dd><p>Returns the wavelength (spatial period) of the wave,
in meters per cycle.
It depends on the medium of the wave.</p>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy</span> <span class="kn">import</span> <span class="n">symbols</span>
<span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy.physics.optics</span> <span class="kn">import</span> <span class="n">TWave</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">A</span><span class="p">,</span> <span class="n">phi</span><span class="p">,</span> <span class="n">f</span> <span class="o">=</span> <span class="n">symbols</span><span class="p">(</span><span class="s1">&#39;A, phi, f&#39;</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">w</span> <span class="o">=</span> <span class="n">TWave</span><span class="p">(</span><span class="n">A</span><span class="p">,</span> <span class="n">f</span><span class="p">,</span> <span class="n">phi</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">w</span><span class="o">.</span><span class="n">wavelength</span>
<span class="go">299792458*meter/(second*f*n)</span>
</pre></div>
</div>
</dd></dl>

<dl class="py property">
<dt class="sig sig-object py" id="sympy.physics.optics.waves.TWave.wavenumber">
<em class="property"><span class="pre">property</span> </em><span class="sig-name descname"><span class="pre">wavenumber</span></span><a class="headerlink" href="#sympy.physics.optics.waves.TWave.wavenumber" title="Permalink to this definition">¶</a></dt>
<dd><p>Returns the wavenumber of the wave,
in radians per meter.</p>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy</span> <span class="kn">import</span> <span class="n">symbols</span>
<span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy.physics.optics</span> <span class="kn">import</span> <span class="n">TWave</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">A</span><span class="p">,</span> <span class="n">phi</span><span class="p">,</span> <span class="n">f</span> <span class="o">=</span> <span class="n">symbols</span><span class="p">(</span><span class="s1">&#39;A, phi, f&#39;</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">w</span> <span class="o">=</span> <span class="n">TWave</span><span class="p">(</span><span class="n">A</span><span class="p">,</span> <span class="n">f</span><span class="p">,</span> <span class="n">phi</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">w</span><span class="o">.</span><span class="n">wavenumber</span>
<span class="go">pi*second*f*n/(149896229*meter)</span>
</pre></div>
</div>
</dd></dl>

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